Simplify the following expression: $ y = \dfrac{-1}{7} - \dfrac{a - 5}{8a + 5} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8a + 5}{8a + 5}$ $ \dfrac{-1}{7} \times \dfrac{8a + 5}{8a + 5} = \dfrac{-8a - 5}{56a + 35} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{a - 5}{8a + 5} \times \dfrac{7}{7} = \dfrac{7a - 35}{56a + 35} $ Therefore $ y = \dfrac{-8a - 5}{56a + 35} - \dfrac{7a - 35}{56a + 35} $ Now the expressions have the same denominator we can simply subtract the numerators: $y = \dfrac{-8a - 5 - (7a - 35) }{56a + 35} $ Distribute the negative sign: $y = \dfrac{-8a - 5 - 7a + 35}{56a + 35}$ $y = \dfrac{-15a + 30}{56a + 35}$